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An expression for the velocity matrix of an electron in the tight-binding approximation is derived for a disordered system by the taking the non-orthogonality between atomic orbitals into account. The velocity matrix has a complicated dependence on the atomic configuration. However, the velocity matrix can be shown to be replaced in the calculation of the DC conductivity by an effective velocity matrix which has an explicit energy dependence but has a simple configuration dependence. The Kubo-Greenwood formula with the effective velocity matrix is very suitable to use in the framework of the Green function theory. Consequently, it turns out that previous formulations of the conductivity made in the 'orthogonal orbital model' can be readily extended in such a way that the effect of the nonorthogonality is fully included.

The authors present the results of Monte Carlo (MC) simulations for the surface properties of the classical one-component plasma. They have used a system of slab geometry for simulating a planar surface and made some improvements over previous work. They have devised a practical method of obtaining the surface energy in the weak coupling regime, where the particle configurations far outside the surface are quite difficult to simulate, and they have improved the sampling efficiency using a modified MC method, which is particularly useful and even indispensable for simulating strongly inhomogeneous systems. Their results for the surface energy show, on contrast to previous results, a proper behavior in the weak coupling regime and a systematic variation with increasing coupling constants, although the density profiles are hardly distinguishable from the previous results.

The density-gradient expansion, one of the approximation schemes of the density functional theory, is used to investigate the influence of finite size on the surface properties of the classical one-component plasma. Variational calculations are performed within the square gradient approximation for the surface properties of a spherical system. It is found that the calculated ion density profile and surface energy for a small sphere are quite different from those for the planar surface in the weak-coupling regime and in good agreement with the recent Monte Carlo simulations. These results provide further support for the previous argument that the Monte Carlo results for a spherical system could be explained, at least in the weak-coupling regime, by taking into account the finiteness of the system as well as the presence of a hard wall introduced for achieving an appropriate equilibrium ion configuration. It is also confirmed that, in the strong-coupling regime, surface properties are not much influenced by the finiteness of a system and by the presence of a hard wall.

The electrical conductivity is calculated in the coherent-potential approximation for the Anderson model, binary alloys and the lattice-gas model. The total conductivity is divided into four terms, each describing a physically distinct process and behaving differently as the degree of disorder varies. One of the partial terms is shown to be identical with the Mott-Hindley-Friedman formula for the electrical conductivity in the random-phase model, and the extent to which the random-phase model formula becomes valid as the degree of disorder increases is discussed.

The Hamiltonian for the ions of a metal can be separated into (i) a structure-dependent part involving all Fourier components of the pseudopotential except the zeroth and (ii) a volume (structure-independent) part to which the zeroth component contributes. For a specified volume, part (i) alone describes the entropy. In earlier work, it was shown that when the observed volumes are used as input information there exists a set of suitably parametrised empty-core pseudopotentials which can be used to calculate the entropies of pure liquid metals and their entropies of mixing. To calculate volumes, both parts (i) and (ii) are needed. It is shown that the pseudopotentials used earlier can be supplemented by nonlocal zeroth Fourier components so as to achieve satisfactory volumes, bulk moduli and thermal expansion coefficients in the pure liquid metals as well as semiquantitative agreement for the excess quantities on mixing.

A self-consistent theory for electron correlations formulated so as to satisfy both the compressibility and spin susceptibility sum rules within the framework of the so-called generalised random phase approximation, is used for studying numerically correlation effects on electron gas properties at metallic densities. The physical implication of the self-consistency requirement in the theory is discussed from the diagrammatic viewpoint of perturbation theory.

The energy bandstructures and charge distributions in CsAu, which is known to show an interesting semiconducting behaviour, are calculated using the APW method. An effect of the charge transfer is taken into account by means of a self-consistent calculation. The calculated bands are characterised by a strong hybridisation of the Cs d state and the Au sp state. They show a metallic behaviour in disagreement with experiments. It has been found that the relativistic energy shifts contribute to the formation of the energy gap between the valence band consisting mainly of the Au s state and the conduction band. The spin-orbit interaction plays a minor role. The way in which CsAu undergoes a nonmetal-metal transition under pressure is suggested.

The extension of the effective medium approximation made by the authors to treat the transport properties of structurally disordered systems is applied to study numerically the DC conductivity of a model liquid metal with a tight-binding single s band of Gaussian atomic orbitals. The non-orthogonality of orbitals is fully taken into account and shown to have appreciable effects. The vertex corrections, which have often been neglected in previous theories, turned out to play very important roles for determining the quantitative as well as qualitative behaviour of the conductivity for the cases of fairly high packing fractions corresponding to ordinary liquid metal densities.

A theory of the electrical conductivity of liquid non-simple metals is formulated based on the tight-binding model by extending the effective medium approximation which is known to be the best single-site theory for the electronic density of states. Special emphasis is given to the consistency between the calculation of the one-particle Green function and that of the response function and the Ward identities connecting both the functions and the related conservation laws prove to be satisfied in the present scheme. Also the formulation is performed in such a way that the extensions to the multi-band, the muffin-tin and the s-d mixing models can be done straightforwardly.

The random-phase model (RPM) due to Mott (1967) and Cohen (1970), which is expected to be valid for a strongly disordered metallic system, is extended to derive an expression of the electrical conductivity for a case with off-diagonal or bond-type disorder where transfer integrals and hence current matrix elements (in the site representation) are random variables. The RPM expression of the electrical conductivity for such a system is not written simply in terms only of the density of states, in contrast to the Mott-Hindley-Friedman formula for the case with only diagonal disorder. Some simple model systems with the bond-type disorder are studied numerically by applying the RPM formula derived here.

The surface properties of the one-component classical plasma (OCP) are re-examined by an approximate method using the density-gradient expansion truncated at second order. The coefficient of the square-gradient term is calculated via the modified hypernetted-chain (MHNC) scheme. It is found that the result is quite different from the previous ones obtained by the Baus-Hansen and mean spherical approximations. The origin of these differences and certain difficulties in the evaluation of this coefficient are discussed in some detail. The present MHNC result for the square-gradient term is used in the variational calculations for the surface density profile and the surface energy. The results of these calculations are in much better agreement than previous ones with Monte Carlo results. The authors also consider the OCP of finite size with a spherically symmetric charge background, for which Monte Carlo simulations have been performed. It is found that the surface energy appropriately defined for such systems shows appreciable size dependences especially for the OCP with small plasma parameters.

A formalism is presented for the calculation, in liquid alloys, of the partial structure factors, the free energies and associated thermodynamic properties. An application is made to NaK alloys with encouraging results.

The authors present the theory of a method for calculating the surface tension gamma of liquid simple metals. The method uses the direct perturbation expansion to second order of the electron-ion pseudopotential. It is found that the second order correction to gamma is significant for liquid metals and that certain important pseudo-atom models which have previously been proposed (Evans and Kumaravadivel (1976), Mon and Stroud (1980)) are inadequate, at least in principle, from a microscopic point of view. The calculated values of gamma for Na and Al are in good agreement with experiment.

The Gibbs-Bogoliubov description of liquid metals together with ideal gas theory for the vapour phase is used to calculate the liquid-vapour coexistence characteristics of sodium. It is found that the method is accurate for pressures below about one atmosphere.

An approximate method is proposed for constructing a one-electron potential for energy-band calculations in which the exchange and correlation effects are included in a compact form in terms of the pair correlation function. The potential is local and naturally divided into the spin-parallel and the spin-antiparallel potentials. Some physical implications of our approximation are discussed especially in comparison with Hedin's screened exchange and Coulomb hole potential.

Edwards' cancellation theorem is re-examined by taking the proper weak-scattering limit of his self-consistent second-order perturbation theory for the electrical conductivity. It is shown that the theory can be rewritten in an equivalent but fully renormalised form, and two important contributions have turned out to be missed out in previous studies. This analysis leads to several correction terms to the famous Ziman formula; in particular, the free-electron mass in the formula is shown to be replaced by the effective mass defined in a natural way.

A simple procedure to extract pseudopotentials from ab initio atomic calculations is presented. The main body of the resulting pseudopotential is completely analytic and fitting the remaining parts to analytic functions is very easy and accurate. The final form of the pseudopotential reduces to a modified form of the optimised Heine-Abarenkov model potential.

It is pointed out that, when the coherent potential approximation is extended to the case of liquid metals by applying the Yonezawa method (1964) for the selfcontained treatment of multiple occupancy corrections in determining the selfconsistent equations for the average Green function and the self energy, the results reduce to the effective medium theory proposed by Roth (1972-4). The approximations involved in this and several previous theories are clarified by means of diagrams in the tight binding representation.

A tight binding formulation is presented for the electronic transport coefficient such as DC conductivity and the Hall coefficient of structurally disordered systems. The formulation is performed with special care about the consistency with the calculation of the electronic density of states. Among existing theories for the density of states the approximation scheme proposed by Ishida and Yonezawa (see Progr. Theor. Phys., vol.99, p.731 (1973)) is especially considered here. Numerical calculations of the conductivity and the Hall coefficient are performed for a model of one hydrogen-like 1s orbital per atom. The atomic distribution function is assumed to be of a random hard-sphere type. A detailed analysis is made for the change of the transport properties with varying input parameters characteristic of the model, i.e. density and the hard-sphere diameter (in units of the effective Bohr radius). The results are also compared with those obtained from the random phase model due to Mott (1967), Hindley (1970) and Friedman (1971).

A theory for the surface tension of liquid metals is developed on the basis of the direct perturbation expansion to second order in the electron-ion pseudopotential. A simple and easily tractable expression for the surface tension is derived from an expression for the Helmholtz free energy which is generalised to a liquid metal with a planar surface. The variational method is used for determining both the electron and ion density profiles at the surface and the bulk radial distribution function is assumed for describing the correlation between ions in the transition zone.

It is shown that the binding energy per valence electron of a simple metal is well described, in atomic units, experimentally and theoretically by the formula a+bz/4rc. Here z is the valency, rc is the empty-core radius, a approximately=0.1 and, in all except the group 1A and 2A cases, 0.9

For pt.I see ibid., vol.11, p.1605 (1981). Based on the general formulation in the effective-medium approximation for transport properties of liquid non-simple metals proposed previously by the authors, a numerical calculation of the DC conductivity is made for a model liquid metal with a tight-binding single s band. It is found that quite large contributions to the conductivity are obtained for the dense packing case from the so called vertex corrections, which have often been neglected in previous studies. The interesting behaviour of the corrections is shown to be understood in terms of their structure factor in a comprehensive manner. The effects of non-orthogonality are also studied. Fairly general conclusions about the transport process in the tight-binding band can be derived from the numerical results.

A microscopic theory is presented to explain how the melting point in metallic small particles is dependent on size. The systems are described by an effective pair interaction of the Gaussian type, constructed to give the basic thermodynamic properties in the bulk metal at low temperatures. The thermodynamic melting temperature, at which the difference between the total Helmholtz free energy of a solid particle and that of a liquid particle of the same mass vanishes, is used as a criterion of the actual melting point in small particles. The variational principle based on the Gibbs-Bogoliubov inequality is used to calculate the Helmholtz free energies of both phases. Applications to the FCC metals Al, Pb and Ag are made and the calculated size dependences of the melting points are similar for all these metals. The result for Pb is in reasonable agreement with experimental data.

The restricted conductivity sum rule is applied to the optical absorption of liquid mercury, by calculating the oscillator strength for the conduction band to 5d core Pauli-forbidden transition. The sum rule suggests that the optical data showing substantial deviation from the Drude theory are quantitatively well supported.